Branched silicone oils have excellent low-temperature characteristics and therein at least three units per molecule of terminal functional groups can be introduced, so that they have hitherto been utilized as hydraulic fluid, such as brake oil, and base oil for curable silicones [as disclosed in the gazettes, e.g., Japanese Tokko Sho 55-21781 (corresponding to U.S. Pat. No. 4,137,189 and GB Patent 1,582,371), Japanese Tokko Sho 59-43515 (corresponding to U.S. Pat. No. 3,833,505 and GB Patent 1,435,161) and Japanese Tokko Sho 59-41394, wherein the term "Tokko" means an "examined patent publication" ]. In recent years, branched silicone oils have also been used as a constituent of a silicone antifoaming agent to substantially extend the duration of antifoaming effect [as disclosed in, e.g., Japanese Tokkai Hei 5-271689 (corresponding to U.S. Pat. No. 5,376,301 and EP Patent 549,232), wherein the term "Tokkai" means an "unexamined published patent application"].
As methods of producing branched silicone oils, there have so far been known the method of condensing hydrolysis products of an alkyltrichlorosilane and a dialkylpolysiloxane in the presence of an equilibration catalyst (European Patent No. 31532), the method of reacting a hydroxyl group-containing organopolysiloxane comprised of R.sub.3 SiO.sub.1/2 units and SiO.sub.2 units with a diorganopolysiloxane having silanol groups at the both ends in the presence of a condensation or equilibration catalyst (European Patent No. 217501), and the method of mixing a diorganopolysiloxane with a vinyl monomer or a vinyl group-containing diorganopolysiloxane and causing a reaction between them by the use of a radical polymerization initiating catalyst (European Patent No. 273448).
However, the branched silicone oils produced by those methods fluctuate in finished viscosity in view of the nature of the reactions, and so they have a drawback of being not consistent in oil characteristics.
In addition, there is known the method of using an alkyltrimethoxysilane or hydrolysis condensates thereof as the source of RSiO.sub.3/2 units and allowing it to undergo the equilibration reaction with a dialkylpolysiloxane. However, the products obtained by such a method are liable to gelation because of the alkoxy groups remaining unreacted. Therefore, that method has a defect that the intended products cannot be obtained consistently.